Formal solutions of singularly-perturbed linear differential systems

Moulay Barkatou (1) , Suzy Maddah (2)

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information
2 SPECFUN - Symbolic Special Functions : Fast and Certified

In this article, we discuss formal invariants of singularly-perturbed linear differential systems inneighborhood of turning points and give algorithms which allow their computation. The algo-rithms proposed are implemented in the computer algebra system Maple.

Mots clés: Singularly-perturbed linear differential system; Turning points; Exponential part; Singularities; Cyclic vectors; Computer algebra; Rank reduction; Formal solutions

Domaines: Mathématiques [math]

Moulay Barkatou, Suzy Maddah. Formal solutions of singularly-perturbed linear differential systems. Journal of Symbolic Computation, 2019, 94, pp.183-209. ⟨10.1016/j.jsc.2018.08.003⟩. ⟨hal-02393887⟩